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3 years ago

Which counter example shows that the following is false? Every perfect square has exactly three factors

1 answer:

4 0

36 is a perfect square, but its factors include 1 and 36, 6 and 6, 4 and 9, 3 and 12, and 2 and 18. that's 9 factors, not 3.

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You go to the mall to make some purchases. You buy 3 dresses which cost $59.99 each and a pair of shoes that cost $75. What is t

mina [271]

Combine costs
59.99(3) + 75 = 179.97 + 75
179.97 + 75 = $254.99 (total cost)
Now add tax: 8% = 0.08
254.99 * 0.08 = 20.3992
254.99 + 20.3992 = 275.3892

Solution: bill would be around $275

6 0

3 years ago

Explau why 3.14 us rational but pi is not

saw5 [17]

If 3.14 is rational, why should pi also be rational ?

The answer to your question is: Because pi is not 3.14 .

8 0

3 years ago

What is the value of 28% of 95?

Bezzdna [24]

It would be 26.6 as the answer

8 0

3 years ago

The polynomial f(x) is written in factored form:

Ray Of Light [21]

Set each set of parentheses to 0 and solve for x.

X—6 = 0

X = 6

X + 5 = 0

X = -5

X-9 = 0

X = 9

The zeros are 6, -5, 9

7 0

3 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago